Mean deviation is a measure of dispersion that calculates the average of the absolute deviations of a set of values from their mean. It is given by the formula:

Mean deviation = Σ|Xi - X̄| / n

Where X̄ is the mean of the values, Xi is each value in the set, and n is the total number of values.

Minimum mean deviation occurs when deviations are taken from the median. This can be explained by the following points:

1. Understanding deviation: Deviation is the difference between each value and a central value such as the mean, median, or mode. When deviations are taken from the mean, some values are above the mean while others are below it. This results in a cancellation effect that can reduce the mean deviation. On the other hand, when deviations are taken from the median, the values above and below it have equal weightage, leading to a balanced distribution of deviations.

2. The median as a measure of central tendency: The median is a measure of central tendency that divides the data set into two equal parts. It is less sensitive to extreme values than the mean and is a better measure of the typical value of the data set. When deviations are taken from the median, they reflect the spread of the data set around the typical value, thus minimizing the mean deviation.

3. Example: Consider the following data set:
10, 20, 30, 40, 50

The mean of this data set is (10+20+30+40+50)/5 = 30.

If deviations are taken from the mean, we get the following values:
|10-30|, |20-30|, |30-30|, |40-30|, |50-30| = 20, 10, 0, 10, 20

The mean deviation in this case is (20+10+0+10+20)/5 = 12.

If deviations are taken from the median, we get the following values:
|10-30|, |20-30|, |30-30|, |40-30|, |50-30| = 20, 10, 0, 10, 20

The median of this data set is 30.

The mean deviation in this case is (20+10+0+10+20)/5 = 12, which is the same as when deviations were taken from the mean.

Thus, we can conclude that the mean deviation is minimum when deviations are taken from the median.

Good question ,
Mean deviation is the arithmetic average of the deviations of the observed values from an average of the observed values.
Mean deviation from the median calculates the arithmetic average of the deviations of the observed values from median of the observed values. Mean deviations is minimum when deviations are taken from median as median is the middle most value of the series and disperse the whole series into minimal value